Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability

Abstract

A computationally efficient procedure for quantifying uncertainty and finding significant parameters of uncertainty models is presented. To deal with the random nature of input parameters of structural models, several efficient probabilistic methods are investigated. Specifically, the polynomial chaos expansion with Latin hypercube sampling is used to represent the response of an uncertain system. Latin hypercube sampling is employed for evaluating the generalized Fourier coefficients of the polynomial chaos expansion. Because the key challenge in uncertainty analysis is to find the most significant components that drive response variability, analysis of variance is employed to find the significant parameters of the approximation model. Several analytical examples and a large finite element model of a joined-wing are used to verify the effectiveness of this procedure.